1. $A=$ $ \left[ {\begin{array}{cc} 6 & -2 & 2\\ -2 & 3 & -1 \\ 0 & 0 & -2\\ \end{array} } \right] $

2. $A=$ $ \left[ {\begin{array}{cc} 8 & -8 & -2\\ 4 & -3 & -2 \\ 3 & -4 & 1\\ \end{array} } \right] $

Subject: Applied Mathematics 4

Topic: Matrices

Difficulty: Medium

1. Characteristic equation of A is $\mid A-\lambda I \mid=0$

$\lambda^3-(12)\lambda^2+36\lambda-32=0$

$\lambda=8,2,2.$

$(\lambda-8)(\lambda-2)(\lambda-2)=0$

Consider $(\lambda-8)(\lambda)=\lambda^2-0\lambda+16$

Now to check that $\lambda^2-10A+16I$

Therefore, consider $A^2-10A+16I$

$= \left[ {\begin{array}{cc} 44 & -20 & 20\\ 20 & 14 & -10 \\ 20 & -10 & 14\\ \end{array} } \right] $-$10\left[ {\begin{array}{cc} 6 & -2 & …